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Full text of "Analytical Mechanics"

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EQUILIBRIUM OF A PARTICLE 17 write them as algebraic equations. Therefore we have the following equations for the analytical form of the condition of equilibrium of a particle. = Zl + Z* + + Zn = 0. (II) The condition of equilibrium may, therefore, be stated in the following form. In order that a particle be in equilibrium the algebraic sum of the components of the forces along each of the axes of a rectangular system of coordinates must vanish. The following rules will be helpful in working out problems on the equilibrium of a particle. First. Represent the particle by a point and the action of each body which acts upon it by a properly chosen force-vector. Be sure that all the bodies which act upon the particle are thus represented. Second. Set the sums of the components of the forces along properly chosen axes equal to zero. Third. If there are not enough equations to determine the unknown quantities, obtain others from the geometrical connections of the problem. Fourth. Solve these equations for the required quantities. Fifth. Discuss the results. ILLUSTRATIVE EXAMPLES. 1. A particle suspended by a string is pulled aside by a horizontal force until the string makes an angle a with the vertical. Find the tensile force in the string and the magnitude of the horizontal force in terms of the weight of the particle. The particle is acted upon by three bodies, namely, the earth, the string, and the body which exerts the horizontal force. Therefore, we * The relation %X = Xi + Xi + + Xn is not an equation. It merely states that 2/Jf is identical with and is an abbreviation for X\ + ZL_ I V 2 T" " * * ~T -An«